
Can you Fix this error in the following image
Require Import Coq.Lists.List.
Import ListNotations.
Section LinkedList.
Variable A : Type.
Inductive LinkedList :=
| LNil
| LCons (x : A) (xs : LinkedList).
End LinkedList.
Section Append.
Fixpoint append (xs ys : LinkedList) : LinkedList :=
match xs with
| LNil => ys
| LCons x xs' => LCons x (append xs' ys)
end.
End Append.
From iris.base_logic Require Import invariants.
From iris.proofmode Require Import tactics.
Section AppendProof.
Context `{!inG Σ (authR (listUR A))}.
Lemma append_nil_r (xs : LinkedList) : append xs LNil = xs.
Proof.
induction xs; simpl; auto.
Qed.
Lemma append_assoc (xs ys zs : LinkedList) :
append (append xs ys) zs = append xs (append ys zs).
Proof.
induction xs; simpl; auto.
rewrite IHxs. reflexivity.
Qed.
Lemma append_comm (xs ys : LinkedList) :
append xs ys = append ys xs.
Proof.
induction xs; simpl; auto.
rewrite IHxs. reflexivity.
Qed.
Lemma append_cons_r (x : A) (xs ys : LinkedList) :
append xs (LCons x ys) = LCons x (append xs ys).
Proof.
induction xs; simpl; auto.
Qed.
End AppendProof.


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